If on dividing 4x² - 3kx + 3 by (x + 2), the remainder is k - 1, then the value of k is :

1. 4

2. -4

3. 3

4. -3

The remainder theorem states that when we divide a polynomial p(x) by (x - a), then the remainder is given by p(a).

Given,

On dividing 4x² - 3kx + 3 by (x + 2), the remainder is k - 1.

⇒ x + 2 = 0

⇒ x = -2.

Substituting x = -2, in 4x² - 3kx + 3, we get remainder (k - 1) :

⇒ 4(-2)² - 3k(-2) + 3 = k - 1

⇒ 4 × 4 + 6k + 3 = k - 1

⇒ 16 + 6k + 3 = k - 1

⇒ 6k + 19 = k - 1

⇒ 6k - k = -1 - 19

⇒ 5k = -20

⇒ k = $-\dfrac{20}{5}$ = -4.

Hence, Option 2 is the correct option.